Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems

In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a "nonsmooth + smooth" composite structure, we further propose an inexact inertial primal-dual method by linearizing the smooth individual function and solving the subproblem inexactly. Assuming merely convexity, we prove that the proposed methods enjoy O(1/k(2)) convergence rate on the objective residual and the feasibility violation in the primal model. Numerical results are reported to demonstrate the validity of the proposed methods.